Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 19, Problem 2AT
Calculate the annual, semiannual, quarterly, and monthly premiums for the following life insurance policies.
| Face Value of | Sex and Age of | Type of | Annual | Semiannual | Quarterly | Monthly | ||||||||
| Policy | Insured | Policy | Premium | Premium | Premium | Premium | ||||||||
| 2. | $55,000 | Female, 21 | 20-Year Endowment | _____ | _____ | _____ | _____ | |||||||
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Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
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(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
Module Code: MATH380202
1. (a) Define the terms "strongly stationary" and "weakly stationary".
Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is
weakly stationary, define the autocorrelation function (acf) Pk, for lag k.
What conditions must a process {X+) satisfy for it to be white noise?
(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of
the following processes {X+} are weakly stationary for t> 0? Briefly justify your
answers.
i. Xt for all > 0.
ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.
(c) Provide an expression for estimating the autocovariance function for a sample
X1,..., X believed to be from a weakly stationary process. How is the autocor-
relation function Pk then estimated, and a correlogram (or acf plot) constructed?
(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where
{E} is a white noise process with variance 1. Compute the population autocorre-
lation function Pk for all k = 0, 1, ....
Chapter 19 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 19.I - Prob. 1TIECh. 19.I - Prob. 2TIECh. 19.I - Prob. 3TIECh. 19.I - Calculate the annual, semiannual, quarterly, and...Ch. 19.I - Calculate the annual. semiannual, quarterly, and...Ch. 19.I - Prob. 3RECh. 19.I - Calculate the annual. semiannual, quarterly, and...Ch. 19.I - Prob. 5RECh. 19.I - Calculate the annual. semiannual, quarterly, and...Ch. 19.I - Calculate the annual. semiannual, quarterly, and...
Ch. 19.I - Calculate the annual. semiannual, quarterly, and...Ch. 19.I - Prob. 9RECh. 19.I - Calculate the value of the nonforfeiture options...Ch. 19.I - Prob. 11RECh. 19.I - Prob. 12RECh. 19.I - Calculate the value of the nonforfeiture options...Ch. 19.I - Calculate the value of the nonforfeiture options...Ch. 19.I - Leroy Kirk is 35 years old and is interested in...Ch. 19.I - 16. Rene Boyer, age 27. wants to purchase a 5-year...Ch. 19.I - Carmen Gutierrez purchased a $75,000, 20-payment...Ch. 19.I - 18. Alex Baron is evaluating his life insurance...Ch. 19.I - Richard Ryan is evaluating his life insurance...Ch. 19.I - BUSINESS DECISION: THE CONSULTATION
20. Tina...Ch. 19.II - You are the insurance agent for Diamond...Ch. 19.II - Prob. 5TIECh. 19.II - Prob. 6TIECh. 19.II - Prob. 7TIECh. 19.II - Prob. 8TIECh. 19.II - Prob. 1RECh. 19.II - Prob. 2RECh. 19.II - Prob. 3RECh. 19.II - Calculate the building, contents, and total...Ch. 19.II - Prob. 5RECh. 19.II - Prob. 6RECh. 19.II - Prob. 7RECh. 19.II - Prob. 8RECh. 19.II - Prob. 9RECh. 19.II - Calculate the short-term premium and refund for...Ch. 19.II - Calculate the short-term premium and refund for...Ch. 19.II - Calculate the short-term premium and refund for...Ch. 19.II - Prob. 13RECh. 19.II - Prob. 14RECh. 19.II - Prob. 15RECh. 19.II - Calculate the amount to be paid by the insurance...Ch. 19.II - Prob. 17RECh. 19.II - Calculate the amount to be paid by the insurance...Ch. 19.II - Prob. 19RECh. 19.II - You are the insurance agent for Castle Mountain...Ch. 19.II - A property insurance policy has an annual premium...Ch. 19.II - 22. Insignia Enterprises has a property insurance...Ch. 19.II - Prob. 23RECh. 19.II - BUSINESS DECISION: BUSINESS INTERRUPTION INSURANCE...Ch. 19.III - Jeff Wasserman, owner of High Performance Racing...Ch. 19.III - Prob. 10TIECh. 19.III - Prob. 1RECh. 19.III - Prob. 2RECh. 19.III - Prob. 3RECh. 19.III - As an insurance agent, calculate the annual...Ch. 19.III - Prob. 5RECh. 19.III - Prob. 6RECh. 19.III - Prob. 7RECh. 19.III - As an insurance agent, calculate the annual...Ch. 19.III - 9. Rick Clinton wants to purchase an automobile...Ch. 19.III -
10. Howard Marshall’s Corvette was hit by a palm...Ch. 19.III - Ben Hoffman has motor vehicle liability insurance...Ch. 19.III - BUSINESS DECISION: INSURING THE FLEET
12. The...Ch. 19 - A mechanism for reducing financial risk and...Ch. 19 - 2. The amount of protection provided by an...Ch. 19 - Prob. 3CRCh. 19 - Prob. 4CRCh. 19 - Prob. 5CRCh. 19 - Prob. 6CRCh. 19 - Prob. 7CRCh. 19 - Prob. 8CRCh. 19 - The premium charged when a policy is canceled by...Ch. 19 - The clause in a property insurance policy...Ch. 19 - Prob. 11CRCh. 19 - Prob. 12CRCh. 19 - Prob. 13CRCh. 19 - Prob. 14CRCh. 19 - Prob. 1ATCh. 19 - Calculate the annual, semiannual, quarterly, and...Ch. 19 - Calculate the annual, semiannual, quarterly, and...Ch. 19 - Calculate the annual, semiannual, quarterly, and...Ch. 19 - Prob. 5ATCh. 19 - Prob. 6ATCh. 19 - Prob. 7ATCh. 19 - 8. Mary Hall purchased a $45,000 20-year endowment...Ch. 19 - Prob. 9ATCh. 19 - Calculate the building, contents, and total...Ch. 19 - Prob. 11ATCh. 19 - Prob. 12ATCh. 19 - Prob. 13ATCh. 19 - Calculate the short-term premium and refund for...Ch. 19 - Prob. 15ATCh. 19 - Calculate the amount to be paid by the insurance...Ch. 19 - Prob. 17ATCh. 19 - Prob. 18ATCh. 19 - Prob. 19ATCh. 19 - Prob. 20ATCh. 19 - Prob. 21ATCh. 19 - Prob. 22ATCh. 19 - Prob. 23ATCh. 19 - Prob. 24AT
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